Related papers: Poisson statistics of eigenvalues in the hierarchi…
We prove a new hypothesis on the conditional distribution of the sample mean of the fluctuations of an i.i.d. random potential in the Anderson model. The paper extends to uniform probability distribution some earlier work with Gaussian…
In this work we analyze the spectral level statistics of the one-dimensional ionic Hubbard model, the Hubbard model with an alternating on-site potential. In particular, we focus on the statistics of the gap ratios between consecutive…
We study the statistical fluctuations of Lyapunov exponents in the discrete version of the non-integrable perturbed sine-Gordon equation, the dissipative ac+dc driven Frenkel-Kontorova model. Our analysis shows that the fluctuations of the…
In this work, we study the spectral statistics for Anderson model on $\ell^2(\mathbb{N})$ with decaying randomness whose single site distribution has unbounded support. Here we consider the operator $H^\omega$ given by $(H^\omega…
We calculate the level statistics by finding the eigenvalue spectrum for a variety of one-dimensional many-body models, namely the Heisenberg chain, the t-J model and the Hubbard model. In each case the generic behaviour is GOE, however at…
We consider orthogonal, unitary, and symplectic ensembles of random matrices with (1/a)(ln x)^2 potentials, which obey spectral statistics different from the Wigner-Dyson and are argued to have multifractal eigenstates. If the coefficient…
This work extends the applications of Anderson-type Hamiltonians to include transport characterized by anomalous diffusion. Herein, we investigate the transport properties of a one-dimensional disordered system that employs the discrete…
We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional…
A one-parameter random matrix model is proposed for describing the statistics of the local amplitudes and phases of electron eigenfunctions in a mesoscopic quantum dot in an arbitrary magnetic field. Comparison of the statistics obtained…
We numerically analyze the random matrix ensembles of real-symmetric matrices with column/row constraints for many system conditions e.g. disorder type, matrix-size and basis-connectivity. The results reveal a rich behavior hidden beneath…
We investigate the top of the spectrum of discrete Anderson Hamiltonians with correlated Gaussian noise in the large volume limit. The class of Gaussian noises under consideration allows for long-range correlations. We show that the largest…
We study the dependence on the spatial dimensionality of different quantities relevant in the description of the Anderson transition by combining numerical calculations in a $3 \leq d \leq 6$ disordered tight binding model with theoretical…
We study the level statistics (second half moment $I_0$ and rigidity $\Delta_3$) and the eigenfunctions of pseudointegrable systems with rough boundaries of different genus numbers $g$. We find that the levels form energy intervals with a…
This note analyzes properties of the median $\nu$ of the Poisson distribution of order $k$. Given a value for the median in the interval $\nu\in[1,k]$, an equation to calculate the corresponding value of the rate parameter $\lambda$ is…
The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete…
Dynamical scaling is an asymptotic property typical for the dynamics of first-order phase transitions in physical systems and related to self-similarity. Based on the integral-representation for the marginal probabilities of a fractional…
We consider one-dimensional discrete Dirac models in vanishing random environments. In a previous work [6], we showed that these models exhibit a rich phase diagram in terms of their spectrum as a function of the rate of decay of the random…
We investigate the statistical properties of the complexness parameter which characterizes uniquely complexness (biorthogonality) of resonance eigenstates of open chaotic systems. Specifying to the regime of isolated resonances, we apply…
The proof of Anderson localization for the 1D Anderson model with arbitrary (e.g. Bernoulli) disorder, originally given by Carmona-Klein-Martinelli in 1987, is based in part on the multi-scale analysis. Later, in the 90s, it was realized…
We discuss the role of rare fluctuation effects in quantum condensed matter systems. In particular, we present recent numerical results of the effect of resonant states in Anderson's original model of electron localization. We find that…